Yahoo Tuning Groups Ultimate Backup mills-tuning-list Question: Equal temperament in ancient China?

Recently on the hpschd-l mailing list, the following discussion
appeared. I'd like to know if people closer to tuning issues can
confirm or deny this origin, and/or provide other references
(preferably in English translation) regarding it. Thanks.

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| Charles E. McElwain mcelwain@world.std.com |
| 33 Vernon Street, Somerville, MA, 02145 (617) 628-5542 |
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------- Exerpt from hpschd-l begins -------------------------------

About a month ago, Tom Parsons wrote:

I read somewhere once (in Barbour?) that e.t. was first worked out by
a Chinese mathematician incredibly far back in the past. And the
author pointed out that in the Chinese musical system there was no
need for it.

(If someone knows more recent scholarship on this, I'd be interested
to hear of it.)

Back in Hong Kong briefly (after trying mostly in vain to log on from
Xi`an, China where I am teaching this semester), I was interested to
see the above reference to China in the equal temperament discussion.
Following is a note from my article, "The Harpsichord and Clavichord
in China during the Ming and Qing Dynasties," in the Westfield Center
for Early Keyboard Studies Newsletter (Oct. 1994):

In Chinese musical philosophy, tuning, and even individual pitches,
held both acoustic and abstract meaning, as well as the power to
transmit physical and spiritual qualities (qi). This helps to
explain Kangxi`s interest in tuning the harpsichords; tuned
instruments signified an orderly empire. There was great
interest in tuning systems; Zhu Zaiyu was the first to describe equal
temperament in China in 1584 (see Kenneth Robinson, A Critical Study of
Chu Tsai-yu`s Contribution to the Theory of Equal Temperament in
Chinese Music (Wiesbaden: Franz Steiner Verlag, 1980).

So it was not so different from the west, where tuning was both a
philosophical as well as practical endeavor. Since Matteo Ricci
brought the first clavichord to China around 1600, the proximity of
these dates open up the possibility that western keyboard instruments
in China during the western baroque period might at some point have
been tuned to equal temperament. On this subject, an American
colleague also teaching here (Prof. Gene Cho, HK Baptist University)
is researching the connection between Matteo Ricci and this Chinese
equal temperament, theorizing that he might have communicated the
Chinese idea back to Europe.

Joyce Lindorff

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🔗masa@gold.interlog.com (marc sabat)

🔗bf250@freenet.carleton.ca (John Sankey)

Gary Morrison <71670.2576@compuserve.com asks
" What the bloody hell is a transcendental number?! "
Another definition is that it's a number that can not be
calculated by any finite number of arithmetic operations (add,
subtract, multiply, divide), i.e. it's one with an infinite
number of terms in *any* series expansion (not just Taylor).
In other words, the decimals go on forever without repeating
with *any* pattern; this lack of pattern is not a lack of
knowledge, but a logical impossibility.

It's a very useful mathematical concept, but, pace Brian, I
think he takes the notion beyond the limits of any practical
tuning into the metaphysical. In fact, if you apply his
comments about Bach's tuning to the post you refer to, he
agrees!

--
John Sankey bf250@freenet.carleton.ca
Music is Beauty, Beauty is Truth, Truth is Freedom

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🔗td@plan9.att.com

bf250@freenet.carleton.ca (John Sankey) guesses:
>Gary Morrison <71670.2576@compuserve.com asks
>>" What the bloody hell is a transcendental number?! "
>Another definition is that it's a number that can not be
>calculated by any finite number of arithmetic operations (add,
>subtract, multiply, divide), i.e. it's one with an infinite
>number of terms in *any* series expansion (not just Taylor).
>In other words, the decimals go on forever without repeating
>with *any* pattern; this lack of pattern is not a lack of
>knowledge, but a logical impossibility.

Not quite. A transcendental number is one that is not
algebraic. That is, it is not a solution of a polynomial
equation with rational coefficients. The smallest non-trivial
set closed under a `finite number of arithmetic operations (add,
subtract, multiply, divide)' is the rational numbers. While
the square root of 12, for example, whose `decimals go on forever
without repeating in *any* pattern', is not rational. Neither
is it transcendental, being a root of the equation x^12=2.

A remarkable fact about transcendental numbers is that, despite
their name, they are as commonplace as numbers get -- the sets
of rational or algebraic numbers are vanishingly small compared
to the transcendentals (first proven by Cantor.)

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🔗Tom <td@...>

td@plan9.att.com babbled:
> While
>the square root of 12, for example, whose `decimals go on forever
>without repeating in *any* pattern', is not rational. Neither
>is it transcendental, being a root of the equation x^12=2.

Obviously, td had a fit of aphasia affecting his puncutation and
whether he was talking about the 12th root of 2 or x^2=12.

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Question: Equal temperament in ancient China?

🔗mcelwain@world.std.com (Charles E McElwain)

🔗masa@gold.interlog.com (marc sabat)

🔗bf250@freenet.carleton.ca (John Sankey)

🔗td@plan9.att.com

🔗Tom <td@...>